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Math  /  Numbers & Operations

Question−12%-12 \%
On effectue une réduction de 12%12 \% Détermine l'évolution réciproque.

Studdy Solution

STEP 1

1. A reduction of 12% 12\% implies a decrease in the original value.
2. We need to find the reciprocal change, which means finding the percentage increase needed to return to the original value after the reduction.

STEP 2

1. Define the initial and reduced values.
2. Calculate the reduced value.
3. Determine the reciprocal percentage increase.

STEP 3

Assume the initial value is 100 100 (a convenient base for percentage calculations).

STEP 4

Calculate the reduced value after a 12% 12\% reduction.
Reduced value=100−12%×100=100−12=88\text{Reduced value} = 100 - 12\% \times 100 = 100 - 12 = 88

STEP 5

Determine the percentage increase needed to return from 88 88 to 100 100 .
Let y be the percentage increase.\text{Let } y \text{ be the percentage increase.} 88×(1+y100)=10088 \times \left(1 + \frac{y}{100}\right) = 100

STEP 6

Solve for y y .
1+y100=100881 + \frac{y}{100} = \frac{100}{88} y100=10088−1\frac{y}{100} = \frac{100}{88} - 1 y100=1288\frac{y}{100} = \frac{12}{88} y=1288×100y = \frac{12}{88} \times 100 y≈13.64y \approx 13.64
The reciprocal percentage increase is approximately:
13.64%\boxed{13.64\%}

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